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3-1 Ordered Pairs
Warm Up
Solve.
1. x – 8 = 19
2. 5 = a – 2
x = 27
a=7
3. 7 + n = 24
n = 17
4. 3c – 7 = 32
c = 13
5. 17y + 7 = 58
y=3
3-1 Ordered Pairs
Problem of the Day
A moving van travels 50 miles per hour.
Use the equation y = 50x, where x
represents the number of hours. How far
will the van travel in 4.5 hours?
225 miles
3-1 Ordered Pairs
Learn to write solutions of equations in two
variables as ordered pairs.
3-1 Ordered Pairs
Vocabulary
ordered pair
3-1 Ordered Pairs
The company that makes team uniforms for a
soccer league charges a $20 fee for team
artwork and $10 for each jersey. Dominic’s
team has 14 players, and Alyssa’s team has 12
players. Find the cost for a set of jerseys for
each team.
Let y be the total cost of a set of jerseys and x
be the number of jerseys needed.
3-1 Ordered Pairs
total cost of jerseys = $20 + $10 •
# of jerseys
y = $20 + $10 • x
Dominic’s team:
y = $20 + ($10 • 14)
y = $160
Alyssa’s team:
y = $20 + ($10 • 12)
y = $140
3-1 Ordered Pairs
An ordered pair (x, y) is a pair of numbers that
can be used to locate a point on a coordinate
plane. A solution of a two-variable equation can
be written as an ordered pair.
The ordered pair (14, 160) is a solution because
160 = $20 + ($10 • 14).
The ordered pair (12, 140) is a solution because
140 = $20 + ($10 • 12).
3-1 Ordered Pairs
Check It Out: Example 1A
Determine whether each ordered pair is a
solution of y = 5x + 3.
(7, 38)
y = 5x + 3
?
38 = 5(7) + 3
?
Substitute 7 for x and 38 for y.
38 = 38 
(7, 38) is a solution.
3-1 Ordered Pairs
Check It Out: Example 1B
Determine whether each ordered pair is a
solution of y = 5x + 3.
(9, 17)
y = 5x + 3
?
17 = 5(9) + 3
?
Substitute 9 for x and 17 for y.
17 = 48 
(9, 17) is not a solution.
3-1 Ordered Pairs
Additional Example 2A: Creating a Table of Ordered
Pair Solutions
Use the given values to make a table of
solutions.
y = x + 3 for x = 1, 2, 3, 4
x
x+3
y
(x, y)
1
1+3
4
(1, 4)
2
2+3
5
(2, 5)
3
3+3
6
(3, 6)
4
4+3
7
(4, 7)
Helpful Hint
A table of solutions
can be set up
vertically or
horizontally.
3-1 Ordered Pairs
Additional Example 2B: Creating a Table of Ordered
Pair Solutions
Use the given values to make a table of
solutions.
n = 6m – 5 for m = 1, 2, 3
m
1
2
3
6m – 5 6(1) – 5 6(2) – 5 6(3) – 5
n
1
7
13
(m, n)
(1, 1)
(2, 7)
(3, 13)
3-1 Ordered Pairs
Check It Out: Example 2B
Use the given values to make a table of
solutions.
n = 8m – 2 for m = 1, 2, 3, 4
m
1
2
3
4
8m – 2 8(1) – 2 8(2) – 2 8(3) – 2 8(4) – 2
n
6
14
22
30
(m, n)
(1, 6)
(2, 14)
(3, 22)
(4, 30)
3-1 Ordered Pairs
Additional Example 3A: Consumer Math Application
A salesman marks up the price of everything
he sells by 20%. The equation for the sales
price p is p = 1.2w, where w is wholesale cost.
What will be the sales price of a sweater with
a wholesale cost of $48?
p = 1.2(48) The wholesale cost of the sweater
before tax is $48. Multiply.
p = 57.6
The $48 wholesale sweater will cost the
customer $57.60, so (48, 57.60) is a solution
of the equation.
3-1 Ordered Pairs
Additional Example 3B: Consumer Math Application
A salesman marks up the price of everything
he sells by 20%. The equation for the sales
price p is p = 1.2w, where w is wholesale cost.
What will be the sales price of a jacket with a
wholesale cost of $85?
p = 1.2(85) The wholesale cost of the jacket
before tax is $85. Multiply.
p = 102
The $85.00 wholesale jacket will cost the
customer $102, so (85, 102) is a solution of
the equation.
3-1 Ordered Pairs
Check It Out: Example 3A
In most states, the price of each item is not
the total cost. Sales tax must be added. If
sales tax is 7.5%, the equation for total cost is
c = 1.075p, where p is the price before tax.
How much will a $22 item cost after sales tax?
c = 1.075(22) The price of the item before tax is
$22. Multiply.
c = 23.65
After sales tax, the $22 item will cost $23.65,
so (22, 23.65) is a solution to the equation.
3-1 Ordered Pairs
Check It Out: Example 3B
In most states, the price of each item is not
the total cost. Sales tax must be added. If
sales tax is 7.5%, the equation for total cost is
c = 1.075p, where p is the price before tax.
How much will a $10 item cost after sales tax?
c = 1.075(10) The price of the item before tax is
$10. Multiply.
c = 10.75
After sales tax, the $10 item will cost $10.75,
so (10, 10.75) is a solution to the equation.
3-1 Ordered Pairs
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
3-1 Ordered Pairs
Warm-up: Countdown to testing week #11
Homework: Page 122 #1-16 all
3-1 Ordered Pairs
Example 1 – I Do
Determine whether each ordered pair is a
solution of y = 4x – 1.
(3, 11)
y = 4x – 1
?
11 = 4(3) – 1 Substitute 3 for x and 11 for y.
11 = 11 
Simplify.
(3, 11) is a solution.
Helpful Hint
The order in which a solution is written is
important. Always write x first, then y.
3-1 Ordered Pairs
Example 2- I Do
Determine whether each ordered pair is a
solution of y = 4x – 1.
(10, 3)
y = 4x – 1
?
3 = 4(10) – 1 Substitute 10 for x and 3 for y.
Simplify.
3 ≠ 39 
(10, 3) is not a solution.
3-1 Ordered Pairs
Example 3- I Do
Use the given values to make a table of
solutions.
y = x + 6 for x = 1, 2, 3, 4
x
x+6
y
(x, y)
1
1+6
7
(1, 7)
2
2+6
8
(2, 8)
3
3+6
9
(3, 9)
4
4+6
10
(4, 10)
3-1 Ordered Pairs
You Do
Determine whether each ordered pair is a
solution of y = 4x – 7.
4. (2, 15) no
5. (4, 9) yes
6. Use the given values to make a table of
solutions. y = 4x  6 for x = 2, 4, 6, 8, and 10
x
4x – 6
y
(x, y)
2
4(2) – 6
2
(2, 2)
4
4(4) – 6
10
(4, 10)
6
4(6) – 6
18
(6, 18)
8
4(8) – 6
26
(8, 26)
10
4(10) – 6
34
(10, 34)
3-1 Ordered Pairs
3-1 Ordered Pairs
Lesson Quiz: Part II
4. A plumbing company charges $50 for a service
call and $15 per hour. They went on a 3-hour job.
How much did the company earn?
c = 15n + 50; $95
3-1 Ordered Pairs
Lesson Quiz for Student Response Systems
1. Which of the following ordered pairs is the
solution of y = 6x – 9?
A. (1, 3)
B. (2, 3)
C. (3, 2)
D. (3, 7)
3-1 Ordered Pairs
Lesson Quiz for Student Response Systems
2. Which of the following ordered pairs is NOT
the solution of y = 4x + 7?
A. (4, 23)
B. (5, 20)
C. (1, 11)
D. (3, 19)
3-1 Ordered Pairs
Lesson Quiz for Student Response Systems
3. Use the given values to identify the table of
solutions.
y = 6x – 4 for x = 1, 3, 5, 7, and 9
A.
B.
3-1 Ordered Pairs
Lesson Quiz for Student Response Systems
4. The water level in a tank is 17 feet. Due to
the heavy rainfall, the water level
increases at the rate of 7 feet per hour.
What will be the water level in the tank
after 5 hours?
A. L = 17n + 17; 102 ft
B. L = 17n + 7; 92 ft
C. L = 7n + 17; 52 ft
D. L = 7n + 7; 42 ft